# Surface Area ad Volume of A Right Circular Cone - Class 9 : Notes

(1) A right circular cone is a solid generated by revolving a line segment which passes through a fixed point which makes a constant angle with a fixed line. The fixed point is called the vertex of the cone,  the fixed line is called the axis of the cone. (2)For a right circular cone of base radius r,  slant height l and height h, we have

(i) Curved surface area $= \pi rl$
For Example:

If radius $r = 5cm$, length $l = 7cm$, then
Curved surface area $= \pi \times 5 \times 7 = 109.9c{m^2}$

(ii) Total surface area $= \pi r(l + r)$
For Example: If radius $r = 5cm$, length $l = 7cm$, then
Total surface area $= \pi \times 5(7 + 5) = 188.4c{m^2}$

(iii) Volume $= {1 \over 3}\pi {r^2}h$
For Example: If radius $r = 5cm$ and height $h = 10cm$, then
Volume $= \frac{1}{3}\pi \times {5^2} \times 10 = 261.66c{m^3}$

Also, Volume $= {1 \over 3}(Area of the base) \times height$
For Example: Volume $= \frac{1}{3}(78.5) \times 10 = 261.66c{m^3}$